In recent years, attention has been paid to a micro-machine (MEMS: Micro Electro Mechanical Systems) element and a small device in which a MEMS element is incorporated. A basic characteristic of the MEMS element is that a driving body included as a mechanical structure is incorporated into a part of the element, and the driving body is driven electrically by an application of coulomb's force between electrodes and the like.
On the other hand, since a micro-oscillation element formed by using a micro-machining technology based on a semiconductor process has such advantages that an area occupied by a device is small, a high Q-value can be obtained, and an integration with another semiconductor device is possible, a use as a high frequency filter in wireless communication devices has been proposed by research laboratories including Michigan University (refer to Non-patent Reference 1).
FIG. 10 shows a schematic view of a resonator, specifically a MEMS resonator, constituting a high frequency filter described. This resonator 1 includes a fixed output electrode 4 formed on a semiconductor substrate 2 through an insulation film 3 and a beam 6 capable of oscillating is formed on an input side to face the output electrode 4 separated by a space 5. The beam 6 has conductivity and is disposed to straddle the output electrode 4 like a bridge to be supported by anchor portions (support portions)8 [8A, 8B] on both the ends.
In this resonator 1, an input terminal t1 is led out from an input electrode 7 connected to an extension portion from the anchor portion 8A of the beam 6, for example, and an output terminal t2 is led out from the output electrode 4, respectively.
In this resonator 1, a high frequency signal S1 is supplied to the beam 6 through the input terminal t1 in the state where a DC bias voltage V1 is applied between the output electrode 4 and the beam 6, and the beam 6 oscillates by electrostatic power generated between the output electrode 4 and the beam 6. A product of a temporal change of capacitance between the output electrode 4 and the beam 6 caused by the oscillation and the DC voltage is output from the output electrode through the output terminal t2. A signal that corresponds to a natural oscillation frequency (resonant frequency) of the beam is output in a high frequency filter.
FIG. 11 is a simulation of a beam structure of the above-described MEMS resonator 1. Portions corresponding to those in FIG. 10 are shown by giving the same reference numerals. A resonant frequency fR of the beam 6 is expressed by a numerical formula 1. In order to obtain a high frequency in the resonator 1, it is necessary to reduce a length L of the beam.
                    fR        =                                            0.162              ⁢              h                                      L              2                                ⁢                                    EK              ρ                                                          [                  Numerical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          1                ]            
L: length of beam (resonator structure)
h: thickness of beam (resonator structure)
E: Young's modulus
K: electromagnetic coupling coefficient
ρ: film density
[Non-patent Reference 1] C. T. -C. Nguyen, “Micromechanical components for miniaturized low-power communication (invited plenary)”, proceedings, 1999 IEEE MTT-S International Microwave Symposium RF MEMS Workshop, Jun. 18, 1999, pp, 48-77.
FIG. 12 shows an equivalent circuit of the above-described MEMS resonator 1. However, a beam is of a cantilever beam type in this MEMS resonator. In this MEMS resonator 1, between the input terminal t1 and the output terminal t2 are inserted in parallel a series circuit of resistance Rx, inductance Lx, and capacitance Cx that constitutes a resonance system, and parasitic capacitance C0 by the space 5 between the beam 6 that is the input electrode and the output electrode 4. When impedance of the resonance system is Zx and impedance of the parasitic capacitance C0 is Z0, an S/N ratio of an output signal is equivalent to Z0/Zx. When a value of Z0/Zx becomes smaller than 1.0, the S/N ratio of the output signal becomes small, because a high frequency signal is transmitted through the impedance Z0 of the parasitic capacitance C0. In the above-described MEMS resonator 1, since the capacitance C0 between the beam 6 and the output electrode 4 before the application of the bias is large, the S/N ratio may be deteriorated.
FIG. 7 is a graph according to a simulation showing a relation between a frequency and Z0/Zx in the resonator. A straight line a with ●-marks being plotted is a characteristic of the above-described resonator 1. The lower the frequency is, the larger the value of Z0/Zx becomes, and when the frequency becomes high and Z0/Zx becomes smaller than 1.0, the resonator 1 does not function as a resonator.
On the other hand, the applicants of the present invention have previously proposed a MEMS resonator in which a large S/N ratio of an output signal is obtained by controlling capacitance C0 between a beam and an output. FIG. 9 shows an example of the MEMS resonator. This MEMS resonator 11 includes: an input electrode 14 into which a high frequency signal S2 is input and an output electrode 15 to output a high frequency signal, which are disposed at a required interval on a semiconductor substrate 12 through an insulation film 13, and a beam capable of oscillating (what is called an oscillation electrode) 17 disposed to face those input and output electrodes 14 and 15 separated by a space 16. The beam 17 is supported by anchor portions (support portions) 18 (18A, 18B) at both ends, and is made into a both-ends-supported beam structure.
In this MEMS resonator 11, a high frequency signal S2 is input into the input electrode 14 through an input terminal t1, a required DC bias voltage V2 is applied to the beam 17, and a high frequency signal of an objective frequency is output from an output terminal t2 which is led out from the output electrode 15. According to this MEMS resonator 11, since facing areas of the input and output electrodes 14 and 15 can be small and an interval between the input and output electrodes 14 and 15 can be large, the parasitic capacitance C0 between the input and output electrodes 14 and 15 becomes small. In addition, in order to obtain a large output signal, the space 16 between the beam 17 and the input and output electrodes 14 and 15 can be made small. Accordingly, the S/N ratio of the output signal can be improved in comparison to the MEMS resonator 1 of the related art shown in FIG. 10.
Hereupon, an oscillation of a second-order mode or higher is used in this MEMS resonator 11. Therefore, when measuring a characteristic of the resonator 11, specifically, when measuring a characteristic ranging from a low frequency to a high frequency, since oscillation may be caused in a first-order mode in a low frequency, there is a possibility that the beam 17 is brought in contact with a lower electrode (input electrode 14, output electrode 15). In other words, since amplitude of the beam 17 becomes larger in the oscillation of the first-order mode than in the oscillation of the second-order mode, there is a possibility that the beam 17 is brought in contact with the lower electrode. If the beam 17 is in contact with the lower electrode, spike current flows in the input electrode 14 and there is a possibility of damaging a peripheral device.